`\color{green} ✍️` In Chapter 2, you have studied different types of polynomials.
One type was the quadratic polynomial of the form `ax^2 + bx + c, a ≠ 0.`
When we equate this polynomial to zero, we get a quadratic equation. Quadratic equations come up when we deal with many real-life situations.
For instance, suppose a charity trust decides to build a prayer hall having a carpet area of `300` square metres with its length one metre more than twice its breadth.
`color(blue)("What should be the length and breadth of the hall ? ")`
Suppose the breadth of the hall is `x` metres. Then, its length should be `(2x + 1)` metres. We can depict this information pictorially as shown in Fig. 4.1.
Now, `color(navy)("area of the hall")` ` = (2x+1) . x \ \m^2 = (2x^2+x) \ \ m^2`
So `2x^2+x = 300` (given)
Therefore `2x^2+x-300 = 0`
So, the breadth of the hall should satisfy the equation `2x^2 +x -300 = 0` which is a quadratic equation.
Many people believe that Babylonians were the first to solve quadratic equations.
For instance, they knew how to find two positive numbers with a given positive sum and a given positive product, and this problem is equivalent to solving a quadratic equation of the form `x^2 – px + q = 0.`
Solving of quadratic equations, in general form, is often credited to ancient Indian mathematicians.
In fact, Brahmagupta (C.E.598–665) gave an explicit formula to solve a quadratic equation of the form `ax^2 + bx = c.`
Later, `color(blue)("Sridharacharya (C.E. 1025)")` derived a formula, now known as the quadratic formula, (as quoted by Bhaskara II) for solving a quadratic equation by the method of completing the square.
`\color{green} ✍️` In this chapter, you will study quadratic equations, and various ways of finding their roots. You will also see some applications of quadratic equations in daily life situations.
`\color{green} ✍️` In Chapter 2, you have studied different types of polynomials.
One type was the quadratic polynomial of the form `ax^2 + bx + c, a ≠ 0.`
When we equate this polynomial to zero, we get a quadratic equation. Quadratic equations come up when we deal with many real-life situations.
For instance, suppose a charity trust decides to build a prayer hall having a carpet area of `300` square metres with its length one metre more than twice its breadth.
`color(blue)("What should be the length and breadth of the hall ? ")`
Suppose the breadth of the hall is `x` metres. Then, its length should be `(2x + 1)` metres. We can depict this information pictorially as shown in Fig. 4.1.
Now, `color(navy)("area of the hall")` ` = (2x+1) . x \ \m^2 = (2x^2+x) \ \ m^2`
So `2x^2+x = 300` (given)
Therefore `2x^2+x-300 = 0`
So, the breadth of the hall should satisfy the equation `2x^2 +x -300 = 0` which is a quadratic equation.
Many people believe that Babylonians were the first to solve quadratic equations.
For instance, they knew how to find two positive numbers with a given positive sum and a given positive product, and this problem is equivalent to solving a quadratic equation of the form `x^2 – px + q = 0.`
Solving of quadratic equations, in general form, is often credited to ancient Indian mathematicians.
In fact, Brahmagupta (C.E.598–665) gave an explicit formula to solve a quadratic equation of the form `ax^2 + bx = c.`
Later, `color(blue)("Sridharacharya (C.E. 1025)")` derived a formula, now known as the quadratic formula, (as quoted by Bhaskara II) for solving a quadratic equation by the method of completing the square.
`\color{green} ✍️` In this chapter, you will study quadratic equations, and various ways of finding their roots. You will also see some applications of quadratic equations in daily life situations.
